Electron orbitals depend on quantized values of energy, angular momentum, and spin. The "shapes" of the orbits represent the probability of an electron being in a certain region, and these shapes are dictated by the solutions to the Schrodinger equation. If you are unfamiliar with the mathematics then that is probably a less than satisfying explanation. There is no satisfactory explanation that relys on classical physics.

Electron orbitals depend on quantized values of energy, angular momentum, and spin. The "shapes" of the orbits represent the probability of an electron being in a certain region, and these shapes are dictated by the solutions to the Schrodinger equation. If you are unfamiliar with the mathematics then that is probably a less than satisfying explanation. There is no satisfactory explanation that relys on classical physics.

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But, the electrons don't orbit in the usual sense, and there is no basis to say that the shapes of the wave functions are elliptical.

But, the electrons don't orbit in the usual sense, and there is no basis to say that the shapes of the wave functions are elliptical.

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That is true and is the reason why I used the word "orbitals". They are not orbits, and they are not circular or elliptical because those are two dimensional forms. Quantum behavior cannot be understood in classical terms.

That is true and is the reason why I used the word "orbitals". They are not orbits, and they are not circular or elliptical because those are two dimensional forms. Quantum behavior cannot be understood in classical terms.

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Yes, and I know that you know that.

I just don't think the OP has phrased a proper question yet. Is he saying that electrons will orbit a nucleus in elliptical orbital paths that are similar to planets orbiting the sun? Or, is he saying something completely different, - like electrons are traveling in a magnetic field and following orbits due to Lorentz force? Or, something else entirely?

I remember doing all this stuff at school when studying physical chemistry.
I have forgotten most of it. I remember that there were 4 different orbitals S,P,D,F and that electrons could have negative or positive spin.
As far as I can remember the Pauling Exclusion principal stated that no two electrons could have exactly the same orbit and spin?
I would be delighted if someone could refresh my memory.

I just don't think the OP has phrased a proper question yet. Is he saying that electrons will orbit a nucleus in elliptical orbital paths that are similar to planets orbiting the sun? Or, is he saying something completely different, - like electrons are traveling in a magnetic field and following orbits due to Lorentz force? Or, something else entirely?

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I was asked as a part of assignment to find out why the electons orbit in an elliptical path similar to that of planets..its based on Sommerfeld's theory ..mathematically it can be proved ..but wanted to know the actual reason behind that theory??

All approaches using "classical Newtonian physics" to calculate electron behavior are doomed to produce results that do not agree with experimental evidence. It matters not how elegant the mathematics if it flies in the face of the evidence.

It is especially odd to think about electron orbits, by analogy to planetary motion, given the uncertainty principle.

I fail to see the pedagogical purpose in giving you such an assignment, but since you're curious I've done some additional research for you.

"The theory was never complete or self-consistent, but was a collection of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics"

In that time period from 1900-1925 Sommerfeld knew that classical physics was inadequate and that small steps were required leading to a giant leap, In 1926 Schrodinger developed the wave equation and "wave mechanics put an end to the era of the old-quantum theory."

from the link u posted Sommerfeld's semiclassical model was based on principle of arbitary invariance(i need to work on that)...so it could overcome some of the limitations of the bohr model..thank you .. though i was aware of the uncertainity principle u just reminded me its the reason why electrons cannot be compared with planetary motion